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Why do center filters and graduated neutral density filters work?

My understanding of optics is poor. What I think I remember, from physics class, is this: light reflects from the subject and hits the front surface of the lens at all points. The lens will focus all of this light into an image at the focus plane. I was told that if you cut a lens in half (top to bottom not front to back) it would still work the same, but the image would be dimmer.

So my question is: why does putting a graduated neutral density or center filter over part of the lens dim only part of the image? It seems it should dim the whole image evenly, but I know it doesn't. So where am I wrong, or what information am I missing?

I am thinking the answer has to do with how far the filter is from the front of the lens, but it is just a guess.

Re: Why do center filters and graduated neutral density filters work?

Think of the light as very small beams hitting the front lens element all parallel to each other. Those that pass through the darker part of the filter are dimmed by the filter and those that don’t are not. What happens inside the lens has nothing to do with it.

As to cutting the lens in half, I don’t see any relevance to the issue of ND filters.

Re: Why do center filters and graduated neutral density filters work?

Larry,

If the filter or grad was located in the entrance pupil of the lens, then it would have equal effect on all parts of the image. As you rightly surmise, they work because they are well in front of the entrance pupil. Those simple optical diagrams you might be thinking of don't show the separation between the front vertex of the lens (the front of the front element) and the entrance pupil.

Look into the front of a lens, and you will see the entrance pupil - it shows the bundle of light going into the lens from whatever angle you are looking from, and it shows you where that bundle of light would pass through a filter. Look from the front and you see the entrance pupil in the centre, look from the side and it is at the periphery of where the filter would be.

In short, the properties you are thinking of for a CF, grad or half-lens only apply to simple lenses, like the imaginary ones used for drawing simple ray diagrams.

Re: Why do center filters and graduated neutral density filters work?

Re: Why do center filters and graduated neutral density filters work?

I'm sure Helen is correct -- you can always take her answers to the bank.

However, I wonder whether, even removed from the lens opening, there isn't some "sharing of light" from all parts of the lens that makes it necessary for centers or grads to really be more heavily tinted than their stated compensating factor. For instance, if you have a one stop grad, is the difference really one stop top to bottom, or more?